The case was brought after an article by Heard in which she claimed to be a victim of domestic abuse.
But Ms Heard's team argued Mr Depp brought her to court simply to "destroy her".
Mr Depp, 58, has denied any abuse and has sued his ex-wife for $50m (£38m).
Ms Heard has in turn, sued him, with a $100m counterclaim.
Hordes of fans have already gathered outside the Virginia court for the trial, expected to last up to seven weeks.
